Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

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        <div xml:id="echoid-div542" type="section" level="1" n="77">
          <head xml:id="echoid-head80" xml:space="preserve">_Notetur autem_,</head>
          <p>
            <s xml:id="echoid-s15272" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15273" xml:space="preserve">Ducta AD ad BH perpendiculari, ſi in hac capiatur AE = _n_;
              <lb/>
            </s>
            <s xml:id="echoid-s15274" xml:space="preserve">ducatúrque EF ad AH parallela; </s>
            <s xml:id="echoid-s15275" xml:space="preserve">hujus cum lineis expoſitis interſe-
              <lb/>
            ctiones æquationum propoſitarum radices exhibebunt reſpectivè; </s>
            <s xml:id="echoid-s15276" xml:space="preserve">erit
              <lb/>
              <note position="left" xlink:label="note-0310-01" xlink:href="note-0310-01a" xml:space="preserve">Fig. 206.</note>
            utique EK, vel EI, vel EM, vel EN æqualis ipſi _a_;
              <lb/>
            </s>
            <s xml:id="echoid-s15277" xml:space="preserve">hoc eſt ipſis AG, concipiendo à ſingula interſectione deduci ad AH
              <lb/>
            perpendiculares, quæ puncta G determinet.</s>
            <s xml:id="echoid-s15278" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15279" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15280" xml:space="preserve">Quò punctum G magîs à termino A removetur (& </s>
            <s xml:id="echoid-s15281" xml:space="preserve">quidem poteſt
              <lb/>
            GA deſumi quavis deſignatâ major) eò ordinatæ GK, GL, GM, GN
              <lb/>
            magìs increſcunt; </s>
            <s xml:id="echoid-s15282" xml:space="preserve">adeo ut quantacunque ponatur AE, parallela EF
              <lb/>
            curvis occurſura ſit; </s>
            <s xml:id="echoid-s15283" xml:space="preserve">& </s>
            <s xml:id="echoid-s15284" xml:space="preserve">proinde ſemper habetur vera radix iſtarum
              <lb/>
            æquationum cuilibet conveniens; </s>
            <s xml:id="echoid-s15285" xml:space="preserve">& </s>
            <s xml:id="echoid-s15286" xml:space="preserve">ea tantùm una, quoniam EF
              <lb/>
            curvas iſtas unico puncto interſecat.</s>
            <s xml:id="echoid-s15287" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15288" xml:space="preserve">3. </s>
            <s xml:id="echoid-s15289" xml:space="preserve">_Curva_ ALL eſt _hyperbola æquilatera_, cujus _axis_ AB, reliquæ
              <lb/>
            AMM, ANN ſunt _hiperboliformes_.</s>
            <s xml:id="echoid-s15290" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15291" xml:space="preserve">4. </s>
            <s xml:id="echoid-s15292" xml:space="preserve">Si AO ſit {1/2} AB; </s>
            <s xml:id="echoid-s15293" xml:space="preserve">& </s>
            <s xml:id="echoid-s15294" xml:space="preserve">AP = {1/3} AB, & </s>
            <s xml:id="echoid-s15295" xml:space="preserve">AQ = {1/4} AB, du-
              <lb/>
            cantúrque OT, PV, QX ad BS parallelæ, erunt hæ curvarum ALL,
              <lb/>
            AMM, ANN _aſymptoti_.</s>
            <s xml:id="echoid-s15296" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15297" xml:space="preserve">5. </s>
            <s xml:id="echoid-s15298" xml:space="preserve">Hinc conſtat in ſecundo gradu fore _a_ &</s>
            <s xml:id="echoid-s15299" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s15300" xml:space="preserve">_n_ - {_b_/2}; </s>
            <s xml:id="echoid-s15301" xml:space="preserve">in tertio _a_&</s>
            <s xml:id="echoid-s15302" xml:space="preserve">gt;
              <lb/>
            </s>
            <s xml:id="echoid-s15303" xml:space="preserve">_n_ - {_b_/3}; </s>
            <s xml:id="echoid-s15304" xml:space="preserve">in quarto _a_&</s>
            <s xml:id="echoid-s15305" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s15306" xml:space="preserve">_n_ - {_b_/4}; </s>
            <s xml:id="echoid-s15307" xml:space="preserve">quæ tamen inæqualitates, ſi AE
              <lb/>
            benemagna ſit, exiguæ erunt.</s>
            <s xml:id="echoid-s15308" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15309" xml:space="preserve">6. </s>
            <s xml:id="echoid-s15310" xml:space="preserve">Æquationibus iſtis nulla competit _maxima, vel minima_.</s>
            <s xml:id="echoid-s15311" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div544" type="section" level="1" n="78">
          <head xml:id="echoid-head81" style="it" xml:space="preserve">Series ſecunda.</head>
          <p>
            <s xml:id="echoid-s15312" xml:space="preserve">_a_ - _b_ = _n_.</s>
            <s xml:id="echoid-s15313" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15314" xml:space="preserve">_aa_ - _ba_ = _nn_.</s>
            <s xml:id="echoid-s15315" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15316" xml:space="preserve">_a_
              <emph style="sub">3</emph>
            - _baa_ = _n_
              <emph style="sub">3</emph>
            .</s>
            <s xml:id="echoid-s15317" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15318" xml:space="preserve">_a_
              <emph style="sub">4</emph>
            - _ba_
              <emph style="sub">3</emph>
            = _n_
              <emph style="sub">4</emph>
            , &</s>
            <s xml:id="echoid-s15319" xml:space="preserve">c.</s>
            <s xml:id="echoid-s15320" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15321" xml:space="preserve">Sit rurſus AB = _b_; </s>
            <s xml:id="echoid-s15322" xml:space="preserve">& </s>
            <s xml:id="echoid-s15323" xml:space="preserve">indefinitè protrahatur AB verſus I, & </s>
            <s xml:id="echoid-s15324" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0310-02" xlink:href="note-0310-02a" xml:space="preserve">Fig. 207.</note>
            ſint anguli RAI, SBI ſemirecti; </s>
            <s xml:id="echoid-s15325" xml:space="preserve">tum concipiantur curvæ BLL,
              <lb/>
            BMM, BNN tales, ut ſi utcunque ducatur GZ ad AI perpendicu-
              <lb/>
            laris (dictas lineas ſecans, utì cernis, punctis K, L, M, N, Z) ſit </s>
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